How to be causal: time, spacetime, and spectra

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical models so that their causal nature /in the sense used here/ should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers Kronig relations applicable not only to just temporal causality, but also to spacetime "light-cone" causality based on signals carried by waves. I also apply this causal reasoning to Maxwell's equations, which is an instructive example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B, cause classification/frames (not in EJP); v7 - unusual model case; v8 add reference

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for

Alternative Histories: Philip Roth and The Plot Against America

This paper deals with Philip Roth’s continual idea of “what if…” with a concentration on his novel, The Plot Against America. Roth has always called himself a suppositional writer, though Roth, (who is Roth?) is a continual presence in his work (Zuckerman and Kepesh, for example, in other writerly personae). Nevertheless, this work makes us question various ideas about twentieth-century American history, not only in terms of the personal, but also in terms of ideas about nationality. This is a novel that is both comic and tragic and which makes us think about our position in the contemporary world of Central and East Europe. More importantly, it makes us think about what is happening in contemporary America. It also questions ideas about Roth as author

Alternative Histories: Philip Roth and The Plot Against America

This paper deals with Philip Roth’s continual idea of “what if…” with a concentration on his novel, The Plot Against America. Roth has always called himself a suppositional writer, though Roth, (who is Roth?) is a continual presence in his work (Zuckerman and Kepesh, for example, in other writerly personae). Nevertheless, this work makes us question various ideas about twentieth-century American history, not only in terms of the personal, but also in terms of ideas about nationality. This is a novel that is both comic and tragic and which makes us think about our position in the contemporary world of Central and East Europe. More importantly, it makes us think about what is happening in contemporary America. It also questions ideas about Roth as author

“Tell everything as it is – no better and no worse:” Images of the West in Washington Irving and Mark Twain

In the United States of the nineteenth-century, the struggle to liberate American writing from European influences took many forms, but one prophecy was that a literature of the West would amount to an American coming of age. The prophecy remains unfulfilled and as one commentator has argued, all the fiction and non-fiction concerning the Frontier “can best be expressed in the image of a Western man straddling his vast empire in splendour, yet standing with his back to the West and looking eastward with awe and reverence” (Robert Lee, From West to East). To explore this proposition, I wish briefly to examine two texts, Washington Irving’s A Tour on the Prairies (1835) and Mark Twain’s Roughing It (1872). In Irving’s Tour, for instance, we are given an account by a well-educated easterner, in which the actual details of Western life and idiom are censored into the picturesque, whilst Twain’s Roughing It is written from the position of a wide-eyed innocent. Both approaches tend to distort the truth. In the work of both authors, the romance of the West takes over from reality and it can be argued that in both cases the disorder of frontier life was kept outside texts, which were written for a predominantly eastern audience. The question posed, then, concerns the way the West was turned into a pastoral world by these authors

“Tell everything as it is – no better and no worse:” Images of the West in Washington Irving and Mark Twain

In the United States of the nineteenth-century, the struggle to liberate American writing from European influences took many forms, but one prophecy was that a literature of the West would amount to an American coming of age. The prophecy remains unfulfilled and as one commentator has argued, all the fiction and non-fiction concerning the Frontier “can best be expressed in the image of a Western man straddling his vast empire in splendour, yet standing with his back to the West and looking eastward with awe and reverence” (Robert Lee, From West to East). To explore this proposition, I wish briefly to examine two texts, Washington Irving’s A Tour on the Prairies (1835) and Mark Twain’s Roughing It (1872). In Irving’s Tour, for instance, we are given an account by a well-educated easterner, in which the actual details of Western life and idiom are censored into the picturesque, whilst Twain’s Roughing It is written from the position of a wide-eyed innocent. Both approaches tend to distort the truth. In the work of both authors, the romance of the West takes over from reality and it can be argued that in both cases the disorder of frontier life was kept outside texts, which were written for a predominantly eastern audience. The question posed, then, concerns the way the West was turned into a pastoral world by these authors

“Tell everything as it is – no better and no worse:” Images of the West in Washington Irving and Mark Twain

In the United States of the nineteenth-century, the struggle to liberate American writing from European influences took many forms, but one prophecy was that a literature of the West would amount to an American coming of age. The prophecy remains unfulfilled and as one commentator has argued, all the fiction and non-fiction concerning the Frontier “can best be expressed in the image of a Western man straddling his vast empire in splendour, yet standing with his back to the West and looking eastward with awe and reverence” (Robert Lee, From West to East). To explore this proposition, I wish briefly to examine two texts, Washington Irving’s A Tour on the Prairies (1835) and Mark Twain’s Roughing It (1872). In Irving’s Tour, for instance, we are given an account by a well-educated easterner, in which the actual details of Western life and idiom are censored into the picturesque, whilst Twain’s Roughing It is written from the position of a wide-eyed innocent. Both approaches tend to distort the truth. In the work of both authors, the romance of the West takes over from reality and it can be argued that in both cases the disorder of frontier life was kept outside texts, which were written for a predominantly eastern audience. The question posed, then, concerns the way the West was turned into a pastoral world by these authors

Alternative Histories: Philip Roth and The Plot Against America

This paper deals with Philip Roth’s continual idea of “what if…” with a concentration on his novel, The Plot Against America. Roth has always called himself a suppositional writer, though Roth, (who is Roth?) is a continual presence in his work (Zuckerman and Kepesh, for example, in other writerly personae). Nevertheless, this work makes us question various ideas about twentieth-century American history, not only in terms of the personal, but also in terms of ideas about nationality. This is a novel that is both comic and tragic and which makes us think about our position in the contemporary world of Central and East Europe. More importantly, it makes us think about what is happening in contemporary America. It also questions ideas about Roth as author